To be truly zero? It would take an infinitely wide or infinitely tall barrier. The particle's wave function is continuous and extends indefinitely, so there is always a nonzero probability of tunneling through. However, the probability decreases to zero so rapidly that in practice, it can be "effectively zero" very easily. If you play with the numbers in the barrier penetration link, you can see just how quickly the probability drops as you increase the barrier height or width.

This is kind of like the Maxwell distribution (or the relativistic Maxwell-Jüttner version) of speeds. Mathematically, the distribution extends to the speed of light, even for a room-temperature gas. But it decreases towards zero so quickly that in practice, no molecule is ever moving anywhere near that fast.

Added: This reasoning also implies that even so-called 'stable' atomic nuclei are actually unstable to some very small degree. We can calculate their half-lives, but they can be vastly longer than the age of the universe!

Some isotopes are fundamentally stable, others are 'virtually-stable'. It depends on the mass-energy of the initial vs. final atom and alpha particle, since just because the particle can tunnel out, doesn't mean it's energetically favorable to do so.

For the building of small nuclei, the way the strong force vs. electrical force works out usually makes it energetically favorable to fuse the nucleons together (assuming a favorable ratio of protons to neutrons, as well). But as the atomic number increases, and given the limited range of the strong force, at some point it starts becoming energetically favorable for particles to tunnel out, so the heavy nuclei decay by fission. But the tricky part is that some isotopes appear 'stable', but actually decay with really long life-times. Bismuth-209 is a great example -- it was calculated to have a half-life of around 1019 years, and this was finally observed only a decade ago. Others have yet to have their decay times experimentally measured.

¹H may be unstable, but for different reasons. Since its nucleus is a single proton, it does not involve alpha decay. Instead it is theorized that protons themselves may be unstable and decay into even smaller particles, but we don't know if this is correct... and if it is correct then all isotopes are unstable, and the half-life is very long, indeed.

They used very sensitive detectors, cooled to only a few millionths of a degree above absolute zero, and observed over several days. In one setting, they used 62g of the isotope, and in another they had 31g. This is a total of 2.7*1023 nuclei, and with a half-life of 1.9*1019 years, you could expect about one decay every 54 minutes. (Hooray for using differential equations to figure that out.) Over 5 days, you could expect about 130 decays, give or take. They measured 128.

This is a total of 2.7*1023 nuclei, and with a half-life of 1.9*1019 years, you could expect about one decay every 54 minutes. (Hooray for using differential equations to figure that out.) Over 5 days, you could expect about 130 decays, give or take. They measured 128.

It's surprising that it is possible to measure every decay, not missing a single one, since alpha particles are so easily stopped and very few would make it outside the bismuth source.

It's surprising that it is possible to measure every decay, not missing a single one, since alpha particles are so easily stopped and very few would make it outside the bismuth source.

maybe they missed few of them, but if you caculate they found out that there is 1 decay every 54 minutes,maybe they saw 1 decay after other in 54 minutes and then next one only 108 minutes later (missed 1)but then they saw other one in short time. and 54 minutes is the average

something i wonder about:there is decaying of elements in our own body?like what if we have inside the body or breath unstable isotops of oxygen that will decay to nytrogen (beta)or Fluorine (minus beta)is that mean our body obtain radiation from decaying elements ?